Intersection Local Times, Loop Soups and Permanental Wick Powers (Memoirs of the American Mathematical Society) free ebook download.

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Intersection Local Times, Loop Soups and Permanental Wick Powers (Memoirs of the American Mathematical Society) free ebook download

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Author(s):	Yves Le Jan

Date:	2017-04-29	Format:	PDF	Language:	English	ISBN/ASIN:	1470436957
Pages:	78	OCR:		Quality:		ISBN13:	9781470436957
Uploader:	alex21s	Upload Date:	9/12/2017 8:50:39 AM

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Several stochastic processes related to transient Levy processes with potential densities $u(x,y)=u(y-x)$, that need not be symmetric nor bounded on the diagonal, are defined and studied. They are real valued processes on a space of measures $\mathcal{V}$ endowed with a metric $d$. Sufficient conditions are obtained for the continuity of these processes on $(\mathcal{V},d)$. The processes include $n$-fold self-intersection local times of transient Levy processes and permanental chaoses, which are `loop soup $n$-fold self-intersection local times' constructed from the loop soup of the Levy process. Loop soups are also used to define permanental Wick powers, which generalizes standard Wick powers, a class of $n$-th order Gaussian chaoses. Dynkin type isomorphism theorems are obtained that relate the various processes. Poisson chaos processes are defined and permanental Wick powers are shown to have a Poisson chaos decomposition. Additional properties of Poisson chaos processes are studied and a martingale extension is obtained for many of the processes described above.

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